If by weather you mean rain and sun, ok. If by weather you mean freezing and snow, there might be a problem. China or pottery or that type of "ceramic" will not last outdoors. The freeze and thaw cycle will crack it and pop the glaze off. True ceramic tile is high fired and less porous than regular china or pottery and due to that will last out of doors.
I assume by shiny you mean a shiny glaze. You could use thinset mortar but it might need some roughing up with sandpaper to get adherence. Thinset is generally preferred out of doors, but good old silicone adhesive caulk is also excellent out of doors and would be my choice.
Further, if you are mosaicing with broken pottery and china, again it can not be exposed to freezing and thawing. I use those materials out of doors and simply bring them in in the fall. an unheated garage or shed is fine as long the item is not exposed to moisture at those temperatures.
I see you are in phoenix? If you dont have cold snowy winters there you are probably fine no matter what you do. I should have looked before I typed all that, LOL

Wacky: You're right. No freezes, maybe little short ones to 32 deg. I didn't think of roughing up the surface. I was simply going to glue/mortar/? pieces on. What a dope. What would you use for roughing it up, and how much?

some coarse sandpaper...that shininess could make your thinset not stick well. But Ive never had a problem with silicone adhering to anything.
you just want the surface to be matte or dull, not slick and shiny.